I will give two solutions, one where everything is cubed and one where just the 3 is cubed, because I don't know what you meant.
Just the 3 is cubed solution(Which I think is correct because it has a nicer answer):
Answer:
[tex]13/2[/tex]
Step-by-step explanation:
We have that [tex]2x+3^3=40[/tex].
We can subtract [tex]3^3=27[/tex] from both sides of the equation to get [tex]2x=13[/tex].
We can then divide by [tex]2[/tex] to get [tex]x=13/2[/tex].
So, [tex]\boxed{x=13/2}[/tex] and we're done!
Everything is cubed solution:
Answer:
[tex]\sqrt[3]{5}-3/2[/tex]
Step-by-step explanation:
We have that [tex](2x+3)^3=40[/tex].
We can take the cube root of both sides to get [tex]2x+3=\sqrt[3]{40}[/tex].
Note that [tex]40=2^3*5[/tex], so [tex]\sqrt[3]{40}=\sqrt[3]{2^3*5}=2\sqrt[3]{5}[/tex].
So, we want to solve [tex]2x+3=2\sqrt[3]{5}[/tex].
We can subtract [tex]3[/tex] from both sides to get [tex]2x=2\sqrt[3]{5}-3[/tex].
We can then divide both sides by [tex]2[/tex] to get [tex]x=\sqrt[3]{5}-3/2[/tex].
So, [tex]\boxed{x=\sqrt[3]{5}-3/2}[/tex] and we're done!
